Transverse cracking in reinforced concrete (R/C) members strengthened by FRP plates and subjected to axial loads is analyzed. A non-linear model is developed, where cohesive stresses in concrete across cracks and non-linear bond–slip law between steel bars and concrete are used. The non-linear governing equations are solved via finite difference method. Comparisons with experimental results confirm the validity of the model. Numerical examples are also presented, simulating tests on plated and unplated R/C members with displacement, force, or crack opening control. The examples show that external FRP-plating is effective in reducing crack width and, consequently, in increasing axial stiffness of tensile members.